If you want to cancel lessons of a month, please let us know before the 20th of the previous month.

Is my sentence correct?

Can prevvious be replaced with either prior or preceding?

Yes this is fine. Previous (note only 1 's') is the best possibility here. 'Preceding' is also possible.

'Prior' cannot be used here. It is not very common. It collocates with 'engagement' ("I'm afraid I can't come to the meeting as I have a prior engagement/commitment" - in other words, I have an other commitment that I organised before you asked me to come to the meeting).
Thanks so much, Ratiatum.